a) \(\left(3x-2\right)\left(3x-1\right)=\left(3x+1\right)^2\)

<=> \(9x^2-9x+2=9x^2+6x+1\)

<=>  \(15x=1\) <=> \(x=\frac{1}{15}\)

b) \(\left(4x-1\right)\left(x+1\right)=\left(2x-3\right)^2\)

<=> \(4x^2+3x-1=4x^2-12x+9\)

<=> \(15x^2=10\) <=> \(x=\frac{2}{3}\)

c) \(\left(5x+1\right)^2=\left(7x-3\right)\left(7x+2\right)\) <=> \(25x^2+10x+1=49x^2-7x-6\)

<=> \(24x^2-17x-7=0\) <=> \(24x^2-24x+7x-7=0\)

<=> \(\left(24x+7\right)\left(x-1\right)=0\) <=> \(\orbr{\begin{cases}x=-\frac{7}{24}\\x=1\end{cases}}\)

d) (4 - 3x)(4 + 3x) = (9x - 3)(1 - x)

<=> 16 - 9x² = 12x - 9x2 - 3

<=> 12x = 19

<=> x = 19/12

e) x(x + 1)(x + 2)(x + 3) = 24

<=> (x² + 3x)(x² + 3x + 2) = 24

<=> (x² + 3x)²  + 2(x² + 3x) - 24 = 0

<=> (x² + 3x)² + 6(x² + 3x) - 4(x² + 3x) - 24 = 0

<=> (x² + 3x + 6)(x² + 3x - 4) = 0

<=> \(\orbr{\begin{cases}x^2+3x+6=0\\x^2+3x-4=0\end{cases}}\)

<=> \(\orbr{\begin{cases}\left(x+\frac{3}{2}\right)^2+\frac{15}{4}=0\left(vn\right)\\\left(x+4\right)\left(x-1\right)=0\end{cases}}\)

<=> \(\orbr{\begin{cases}x=-4\\x=1\end{cases}}\)

g) (7x - 2)² = (7x - 3)(7x + 2)

<=> 49x² - 28x + 4 = 49x² - 7x - 6

<=> 21x = 10 <=> x = 10/21

a: \(\Leftrightarrow9x^2-9x+2=9x^2+6x+1\)

=>-3x=-1

hay x=1/3

b: \(\Leftrightarrow4x^2+4x-x-1=4x^2-12x+9\)

=>3x-1=-12x+9

=>15x=10

hay x=2/3

c: \(\Leftrightarrow25x^2+10x+1=25x^2+25x-x-1=24x-1\)

=>10x-24x=-1-1

=>-14x=-2

hay x=1/7

d: \(\Leftrightarrow49x^2-28x+4=49x^2+14x-21x-6\)

=>-28x+4=-7x-6

=>-21x=-10

hay x=10/21

a. \(\left(3x-2\right)\left(3x-1\right)=\left(3x+1\right)^2\)

\(\Leftrightarrow9x^2-9x+2=9x^2+6x+1\)

\(\Leftrightarrow-3x=-1\)

\(\Leftrightarrow x=3\)

b.

\(\left(4x-1\right)\left(x+1\right)=\left(2x-4\right)^2\)

\(\Leftrightarrow4x^2+3x-1=4x^2-16x+16\)

\(\Leftrightarrow19x=17\)

\(\Leftrightarrow x=\dfrac{17}{19}\)

a: \(=2x^3:\dfrac{-3}{2}x+4x:\dfrac{3}{2}x-5:\dfrac{3}{2}\)

=-4/3x^2+8/3-10/3

=-4/3x^2-2/3

d: \(\dfrac{3x^3-5x+2}{x-3}=\dfrac{3x^3-9x^2+9x^2-27x+22x-66+68}{x-3}\)

\(=3x^2+9x+22+\dfrac{68}{x-3}\)

\(a. 2x(3x^2-5x+3) = 6x^3-10x^2+6x \)

\(b. -2x(x^2+5x-3) = -2x^3-10x^2+6x\)

c. \(-\dfrac{1}{2}x^2\left(2x^3-4x+3\right) =-x^5+2x^3-\dfrac{3}{2}x^2\)
\(d.\left(2x-1\right)\left(x^2+5-4\right)=\left(2x-1\right)\left(x^2+1\right)=2x^3+2x-x^2-1\)
e. \(-\left(5x-4\right)\left(2x+3\right)=10x^2+15x-8x-12=-10x^2+7x-12\)

f.\(\left(2x-y\right)\left(4x^2-2xy+y^2\right)=\left(2x-y\right)\left(2x-y\right)^2=\left(2x-y\right)^3\)

g.\(\left(3x-4\right)\left(x+4\right)+\left(5-x\right)\left(2x^2+3x-1\right)=3x^2+12x-4x-16+10x^2+15x-5-2x^3-3x^2+x=-2x^3+10x^2+24x-21\)

e. \(7x\left(x-4\right)-\left(7x+3\right)\left(2x^2-x+4\right)=7x^2-28x-14x^3+7x^2-28x-6x^2+3x+-12=-14x^3+8x^2-53x-12\)

1.

a.\(\Leftrightarrow7x-5x=3+12\)

\(\Leftrightarrow2x=15\Leftrightarrow x=\dfrac{15}{2}\)

b.\(\Leftrightarrow6x-10-7x-7=2\)

\(\Leftrightarrow x=-19\)

c.\(\Leftrightarrow1-3x=4x-3\)

\(\Leftrightarrow7x=2\Leftrightarrow x=\dfrac{2}{7}\)

d.\(\Leftrightarrow8x^2-4x+12x-6-8x^2-8x-2=12\)

\(\Leftrightarrow-2=12\left(voli\right)\)